When dynamical encounters take place within dense environments such as globular clusters, it is likely that some of the remnant BHs are retained in the cluster and merge in a subsequent dynamical encounter, contributing to the hierarchical merger population. The authors of [1]} find that, for a broad range of populations considered, 16% of mergers in the hierarchical merger population have \(\chi _{\rm eff} < -0.3\) . Using our inferred \(\chi _{\rm eff}\)  distribution we infer \(2.1\%^{+3.9\%}_{-1.5\%}\)  of BBH mergers have \(\chi _{\rm eff} < -0.3\) . Using this interpretation from the \(\chi _{\rm eff}\)  distribution, we place a conservative upper limit on the contribution of hierarchical mergers to the BBH merger population of \({13\%}^{+24\%}_{-9\%}\)  which agrees with the one obtained when using just the spin magnitude information. This limit broadly agrees with the upper limit of 26% for the fraction of hierarchical mergers presented in [1]}, in which the authors use parametric models to infer the \(\chi _{\rm eff}\)  distribution.
This is also consistent with the results of [3]} who found that depending on the escape velocity of the hierarchical merger environment up to \(\approx 10\%\)  of merging black holes may come from hierarchical mergers.
